Calculate the product below and give your answer in scientific notation. $ {\left(3.3\times 10^{-4} \right) \times \left(8.0\times 10^{0} \right) =\ ?} $
Solution: Start by collecting the significands and exponents. $ ({3.3} \times {10^{-4}}) \times ({8.0} \times {10^{0}}) = ({3.3} \times {8.0}) \times ({10^{-4}} \times {10^{0}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {26.4} \times {10^{-4 \,+\, 0}}$ $= {26.4} \times {10^{-4}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${26.4}$ is the same as ${2.64 \times 10}$ or ${2.64 \times 10^{1}}$. $ = {2.64 \times 10^{1}} \times {10^{-4}} $ $ = 2.64 \times 10^{{1} + {-4}} $ $= 2.64\times 10^{-3}$